Summary

Typical well logs show that formation electrical resistivity varies substantially as a function of depth in the earth. These variations consist typically of slow-scale macroscopic changes or trends, modulated by rapid variations due to fine scale layering. The rapidly varying resistivity fluctuations are significant in amplitude and occur over small spatial scales, down to the resolution of the logging tool. Using a plane stratified earth model, we examine the effects of this fine scale microstructure on the scattering of the naturally occurring electromagnetic waves used in magnetotellurics (MT). We show theoretically how MT data are influenced by the multiscale nature of the formation resistivity. MT data may be viewed as arising largely from a smoothed “effective medium” version of the resistivity vs. depth profile. The difference between the data produced by the actual medium and that produced by the effective medium is due to scattering noise arising from the layering microstructure. We model this fine scale layering as a rapidly varying stochastic process. This scattering noise component of MT data is fundamental since it arises from the very structure of the medium being probed. This noise is substantial at frequencies above ≈0.1Hz and has unique statistical properties, which we characterize. We assess the impact of this noise upon the detectability of a thin layer of increased resistivity at depth. We show that the theory agrees well with Monte Carlo simulations.